Pumped storage is geographically dependent. Batteries are nowhere near cost effective. "Demand shifting" is also hugely expensive: you can't just cut industrial inputs without causing adverse effects throughout the economy.
Nuclear power is dispatchable enough to satisfy grid usage. The difference between peak and minimum demand is typically 20-30%. And it's a pretty gradual transition, happening over the span of multiple hours. You're right, you can't just crank nuclear from 0 to 100% in an hour like a gas turbine, but a 100% nuclear grid is totally doable by overcooling the turbines to reduce outputs during low demand. The French have successfully used nuclear for over 85% of their electricity, so this is demonstrably capable.
The cost effective way would be with wind farms, pumped/battery storage and demand shifting.
(this would be a nice problem to have, by the way, but we are STILL churning through terawatt hours of gas while the sun is shining and the wind is blowing all over).
Nuclear power isnt dispatchable. It's not just 5x more expensive. It would overproduce during times when we don't need electricity and underproduce when we do.